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arXiv:1303.1611 · WORLD SCIENTIFIC eBooks

EXACTLY SOLVABLE BCS-BEC CROSSOVER HAMILTONIANS

A. BIRRELL, Phillip S. Isaac, Jon Links

Published Aug 14, 2013• 0 citations
arXivHTMLPDF

Abstract

We demonstrate a novel approach that allows the determination of very general classes of exactly solvable Hamiltonians via Bethe ansatz methods. This approach combines aspects of both the co-ordinate Bethe ansatz and algebraic Bethe ansatz. The eigenfunctions are formulated as factorisable operators acting on a suitable reference state. Yet, we require no prior knowledge of transfer matrices or conserved operators. By taking a variational form for the Hamiltonian and eigenstates we obtain general exact solvability conditions. The procedure is conducted in the framework of Hamiltonians describing the crossover between the low-temperature phenomena of superconductivity, in the Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC).

DOI
10.1142/9789814518550_0018

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